In a speech from the Senate floor, Reid said a vote on the amendment would be held sometime in the summer, after the Senate Judiciary Committee marks up the amendment in the coming weeks. Reid also said there would be hearings on the amendment, giving Democrats a chance to elevate the campaign-finance issue to a higher profile in the thick of campaign season.

"Every American should have the same ability to influence our political system," Reid said Thursday. "One American, one vote. That's what the Constitution guarantees. The Constitution does not give corporations a vote, and the Constitution does not give dollar bills a vote."

Democrats announced the amendment, which is being sponsored by New Mexico Sen. Tom Udall, late last month. It would give back authority to Congress and state governments in regulating campaign spending, and also would allow Congress to pass campaign-finance reform legislation that withstands constitutional challenges.

In doing so, the amendment would reverse some major recent Supreme Court decisions on campaign finance, including 2010's Citizens United case and the recentMcCutcheon v. FEC ruling. Those decisions have eliminated limits on millions of dollars' worth of donations to political campaigns from corporations, labor unions, and generally wealthy individuals.

"More and more we see Koch Industries — Americans for Prosperity, one of their shadowy front groups — dictating the results of primaries and elections across the country," Reid said. "Behind these nonvoting organizations are massively wealthy men hoping for a big monetary return on their political donations. When the candidates they bankroll get into office, the winners inevitably begin to legislate their sponsor's business plans. Less regulations, less overnight for corporations."

Despite Reid's heated rhetoric, it's extremely unlikely Udall's amendment will ever become part of the U.S. Constitution. It would need to be passed by two-thirds of both the House and Senate, as well as ratified by three-quarters of the states. But the high-profile nature of the amendment keeps one of Democrats' main messaging tools front and center in the midst of the campaign.

Senate Minority Leader Mitch McConnell characterized the amendment as an "all-out assault on the right to free speech."

"It’s also a clear sign of just how desperate elected Washington Democrats have become in their quest to hold onto power," McConnell said in a statement. "Proposing to take away this fundamental right from the American people and vest it in the federal government instead is the ultimate act of radicalism, and it should concern all Americans who care about their right to speak their minds and to participate freely in the political process."